Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3. The second column is labeled y with entries one-tenth, one-half, five-halves, StartFraction 25 Over 2 EndFraction, StartFraction 125 Over 2 EndFraction What is the rate of change of the function described in the table? Twelve-fifths 5 StartFraction 25 Over 2 EndFraction 25

Answer 1

The rate of change of the function is found by dividing the change in y by the change in x between any two points. Using the first and last points of the table, the rate of change is calculated as 1249/80.

Step-by-step explanation:

The rate of change of a function can be found by taking the difference in y-values divided by the difference in x-values between any two points on the function. Therefore, to find the rate of change given the table of values, we can use the formula:

Rate of Change = (y₂ - y₁) / (x₂ - x₁)

Using the first and last entries from the data table provided:

Let x₁ = -1 and y₁ = 1/10, and let x₂ = 3 and y₂ = 125/2. Plugging these into our formula, we get:

Rate of Change = (125/2 - 1/10) / (3 - (-1))

First, we simplify the difference in y-values:

125/2 - 1/10 = (1250 - 1) / 20 = 1249/20

Next, the difference in x-values is:

3 - (-1) = 4

Finally, we divide the difference in y-values by the difference in x-values:

1249/20 / 4 = 1249/80

Therefore, the rate of change of the function described in the table is 1249/80.